Play around with different departure cities, and then see if you can find a low-cost carrier to that point from YYG.

On my last trip, I priced DL's nonstop from MSP and found the price to be outrageous. So I played around with other possible cities to leave from and found that flights out of LAX were significantly cheaper than any others. I book at flight LAX-NRT and then found a cheap flight MSP-LAX. I saved hundreds of dollars, even with staying overnight near LAX.